A permanent with indestructible can’t be destroyed, but it can still be sacrificed, exiled, put into a graveyard, and so on. Notably, a permanent with indestructible can be put into its owner’s graveyard due to the “legend rule.”

11/17/2017

Creatures with indestructible still have damage marked on them, even though that damage won’t destroy them. If Avacyn leaves the battlefield, creatures that lose indestructible and have lethal damage marked on them will be destroyed.

11/17/2017

A creature with 0 toughness is put into its owner’s graveyard even if it has indestructible.

11/17/2017

A planeswalker with indestructible still loses loyalty as it’s dealt damage. It is put into its owner’s graveyard if its loyalty becomes 0.